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Geometry Question Paper
Geometry
Course:Certificate In Bridging Mathematics
Institution: Kca University question papers
Exam Year:2012
1
UNIVERSITY EXAMINATIONS: 2011/2012
EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS
MAT 102 GEOMETRY
DATE: APRIL 2012 TIME: 1½ HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE (30 MARKS) (COMPULSORY)
a) Vector p is given as p=ni-2j+k. If p = 21 , find the value of n (3 Marks)
b) A circle of radius 6cm has a chord 10cm long. Find
i) The angle subtended at the centre of the circle by the chord (3 Marks)
ii) The arc length subtending the angle at the centre (2 Marks)
c) Show that 3cos2?+5sin2?=3+2sin2? (3 Marks)
d) p(300N,730E) and Q(300N,1070W) are two towns on the surface of the earth. Find the distance
in kilometers between them.
i) Along the parallel of latitude (3 Marks)
ii) Along a great circle (3 Marks)
e) AB and XY are two intersecting chords of a circle. They meet at R such that AR = 4cm, XR=5cm
and RY = 3cm. Calculate the length of AB. (4 Marks)
f) Draw a triangle ABC such that ?ABC=500 , BC = 4cm and AB = 5cm. Produce BA to P and BC to
Q. Join AC (3 Marks)
i) Draw an escribed circle touching lines BAP, AC and BCQ. (4 Marks)
ii) Measure the radius of the circle (2 Marks)
2
QUESTION TWO (15 MARKS)
a) Given that 00=? =900, solve the equation 4cos2?-4cos?+1=sin2? (5 Marks)
b) The length of the sides of an inscribed triangle are 10cm, 7cm and 5cm respectively. Calculate
i) The sizes of the angles of the triangle (8 Marks)
ii) The radius of the circle (2 Marks)
QUESTION THREE (15 MARKS)
A point A lies on the latitude 500N and longitude 100W, B lies on latitude 500N and 850W and C lies on
350S and 100W. Calculate
i) The distance between A and C along a great circle (3 Marks)
ii) The radius of the parallel of latitude 500N (3 Marks)
iii) The distance between A and B along a parallel of latitude (3 Marks)
iv) The distance of B from the equator (3 Marks)
v) The length of the chord AB (3 Marks)
QUESTION FOUR (15 MARKS)
a) Show that points S(2, 4,6), T (1, 2,3) and U (-12,-1,-32) are collinear (5 Marks)
b) At a point A, Richard records the angle of elevation of the top (T) of the building as 220. He moves
further from the building by 28m to point B and notes that the angle of elevation of the top then is
180. Determine
i) The height of the building (5 Marks)
ii) How far he is from the bottom of the building when the angle of elevation of the top T is 100
(5 Marks)
QUESTION FIVE (15 MARKS)
In a quadrilateral OACB, OA = a and OB = b. OA is parallel to BC. OA=3BC and M is a point on AB
such that AM:MB = 3:1.
i) Evaluate the vectors AB, BM, OM and MC in terms of a and b (12 Marks)
ii) Show that O, M and C are collinear. (3 Marks)
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